Details

Time bar (total: 21.8s)

sample256.0ms

Algorithm
intervals
Results
135.0ms1281×body80nan
56.0ms405×body80valid

simplify187.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05417
117417
271017
3494017
4500217

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.1b

localize33.0ms

Local error

Found 4 expressions with local error:

6.8b
(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
10.9b
(pow (/ d h) (/ 1.0 2.0))
11.1b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
13.8b
(pow (/ d l) (/ 1.0 2.0))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
205×add-exp-log
107×prod-exp
55×div-exp
45×times-frac
40×add-sqr-sqrt add-cube-cbrt *-un-lft-identity pow-exp
30×add-cbrt-cube
26×unpow-prod-down pow-unpow
16×associate-*r*
14×pow-to-exp
13×cbrt-unprod
10×pow1
5×cbrt-undiv div-inv
4×add-log-exp
3×associate-*r/ associate-*l/
2×distribute-rgt-in sub-neg pow-pow distribute-lft-in associate-*l* pow-prod-down *-commutative sqr-pow
1×frac-times flip3-- flip--
Counts
4 → 176
Calls
4 calls:
13.0ms
(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
5.0ms
(pow (/ d h) (/ 1.0 2.0))
13.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
5.0ms
(pow (/ d l) (/ 1.0 2.0))

series1.5s

Counts
4 → 12
Calls
4 calls:
635.0ms
(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
68.0ms
(pow (/ d h) (/ 1.0 2.0))
738.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
67.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify46.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
012282042
150011847

prune749.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 12.3b

localize50.0ms

Local error

Found 4 expressions with local error:

4.8b
(/ (* M D) (* 2.0 d))
6.8b
(* (* (pow (/ d h) (/ 1.0 2.0)) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
10.9b
(pow (/ d h) (/ 1.0 2.0))
11.1b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
738×add-exp-log
487×prod-exp
216×pow-exp
171×div-exp
78×pow-to-exp
46×add-cbrt-cube
28×times-frac
26×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
20×cbrt-unprod
16×associate-*r*
13×unpow-prod-down pow-unpow
9×pow1 cbrt-undiv
4×div-inv add-log-exp
3×associate-*r/ associate-*l/
2×distribute-rgt-in sub-neg distribute-lft-in associate-*l* pow-prod-down *-commutative
1×frac-times flip3-- pow-pow frac-2neg clear-num associate-/r* flip-- associate-/l* sqr-pow
Counts
4 → 260
Calls
4 calls:
6.0ms
(/ (* M D) (* 2.0 d))
28.0ms
(* (* (pow (/ d h) (/ 1.0 2.0)) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
5.0ms
(pow (/ d h) (/ 1.0 2.0))
12.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.5s

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ (* M D) (* 2.0 d))
631.0ms
(* (* (pow (/ d h) (/ 1.0 2.0)) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
69.0ms
(pow (/ d h) (/ 1.0 2.0))
733.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify77.0ms

Algorithm
egg-herbie
Counts
272 → 272
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
016745564
150015223

prune771.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 11.3b

localize55.0ms

Local error

Found 4 expressions with local error:

2.7b
(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0))
4.8b
(/ (* M D) (* 2.0 d))
6.8b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) h) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
11.1b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite253.0ms

Algorithm
rewrite-expression-head
Rules
5483×add-exp-log
4085×prod-exp
1997×pow-exp
1387×div-exp
643×pow-to-exp
232×1-exp
55×add-cbrt-cube
27×cbrt-unprod
20×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
16×associate-*r*
13×pow-unpow
12×pow1
9×cbrt-undiv
5×unpow-prod-down
4×pow-prod-down div-inv add-log-exp
3×associate-*r/ associate-*l/
2×distribute-rgt-in sub-neg distribute-lft-in associate-*l* *-commutative
1×frac-times flip3-- pow-pow frac-2neg clear-num associate-/r* flip-- associate-/l* sqr-pow
Counts
4 → 983
Calls
4 calls:
11.0ms
(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0))
6.0ms
(/ (* M D) (* 2.0 d))
67.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) h) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
16.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.1s

Counts
4 → 12
Calls
4 calls:
119.0ms
(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0))
28.0ms
(/ (* M D) (* 2.0 d))
977.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) h) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
946.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify305.0ms

Algorithm
egg-herbie
Counts
995 → 995
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
0411133873
1500333679

prune882.0ms

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 10.4b

localize60.0ms

Local error

Found 4 expressions with local error:

4.8b
(/ (* M D) (* 2.0 d))
5.6b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
6.8b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) h) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (/ 1 l))))
7.5b
(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (/ 1 l))

rewrite267.0ms

Algorithm
rewrite-expression-head
Rules
5734×add-exp-log
4256×prod-exp
2022×pow-exp
1445×div-exp
648×pow-to-exp
248×1-exp
75×add-cbrt-cube
40×cbrt-unprod
19×associate-*r*
16×pow1 rec-exp
13×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
11×cbrt-undiv
10×times-frac
7×pow-prod-down associate-*l/
4×add-log-exp
3×associate-*r/ associate-*l* *-commutative
2×distribute-rgt-in sub-neg distribute-lft-in div-inv
1×frac-times flip3-- frac-2neg clear-num associate-/r* un-div-inv flip-- associate-/l*
Counts
4 → 1020
Calls
4 calls:
6.0ms
(/ (* M D) (* 2.0 d))
10.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
66.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) h) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (/ 1 l))))
15.0ms
(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (/ 1 l))

series2.5s

Counts
4 → 12
Calls
4 calls:
34.0ms
(/ (* M D) (* 2.0 d))
754.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
972.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) h) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (/ 1 l))))
753.0ms
(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (/ 1 l))

simplify313.0ms

Algorithm
egg-herbie
Counts
1032 → 1032
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
0423135131
1500234916

prune680.0ms

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 10.3b

regimes1.3s

Accuracy

5.9% (5.9b remaining)

Error of 16.4b against oracle of 10.5b and baseline of 16.8b

bsearch372.0ms

Steps
ItersRangePoint
8
1.0338094857556896e+27
5.618644324858641e+31
3.1925120038287596e+28
4
-2.920750373954428e-133
-1.755670850222093e-133
-2.0794825451855812e-133

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
077120
177120

end0.0ms

sample7.5s

Algorithm
intervals
Results
4.0s38195×body80nan
1.8s12716×body80valid